Research Papers - De-Jun Feng (Updated December 09, 2023).

  1. Erdos similarity problem via bi-Lipschitz embedding. Preprint, 2023.
  2. Typical self-affine sets with non-empty interior. Preprint, 2022. To appear in Asian. J. Math. (with Zhou Feng)
  3. Dimensions of projected sets and measures on typical self-affine sets. Adv. Math. 431(2023), Paper No. 109237. (with Chiu-Hong Lo and Cai-Yun Ma)
  4. A separation property for iterated function systems of similitudes. Methods and Applications of Analysis. 30 (2023), no. 1, 17--26. (with Huo-Jun Ruan and Ying Xiong)
  5. Dimension of invariant measures for affine iterated function systems. Duke Math. J. 172 (2023), no. 4, 701--774.
  6. Dimension estimates for $C^1$ iterated function systems and repellers. Part I. Ergodic theory Dynam. Systems 43(2023), 2673--2706. (with Karoly Simon)
  7. Dimension estimates for $C^1$ iterated function systems and repellers. Part II. Ergodic theory Dynam. Systems 42 (2022), no. 11, 3357--3392. (with Karoly Simon)
  8. Estimates on the dimension of self-similar measures with overlaps. J. Lond. Math. Soc. 105 (2022), no. 4, 2104--2135. (with Zhou Feng)
  9. On arithmetic sums of fractal sets in ${\Bbb R}^d$. J. Lond. Math. Soc. 104(2021), no. 1, 35-65. (with Yufeng Wu)
  10. Dimensions of random statistically self-affine Sierpinski sponges in $\mathbb R^k$. J. Math. Pure. Appl. 149 (2021), 254--303. (with Julien Barral)
  11. On multifractal formalism for self-similar measures with overlaps. Math. Z. 298 (2021), no. 1-2, 359--383. (with Julien Barral)
  12. On the Hausdorff Dimension of Bernoulli Convolutions Int. Math. Res. Not. IMRN. 2020 (2020), no. 19, 6569--6595. (with Shigeki Akiyama, Tom Kempton and Tomas Persson)
  13. Uniformity of Lyapunov exponents for non-invertible matrices. Ergodic theory Dynam. Systems 40 (2020), no. 9, 2399-2433. (with Chiu-Hong Lo and Shuang Shen)
  14. Affine embeddings of Cantor sets and dimension of $\alpha\beta$-sets. Israel J. Math. 226 (2018), no. 2, 805--826. (with Ying Xiong)
  15. Self-affine sets in analytic curves and algebraic surfaces Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 1, 109--119. (with Antti Kaenmaki)
  16. Dimensions of random covering sets in Riemann manifolds Ann. Probab. 46 (2018), no. 3, 1542--1596. (with Esa Jarvenpaa, Maarit Jarvenpaa and Ville Suomala)
  17. Projections of planar Mandelbrot measures Adv. Math. 325(2018), 640--718. (with Julien Barral)
  18. Variational principles for weighted topological pressure. J. Math. Pure. Appl. 106 (2016), 411--452. (with Wen Huang)
  19. On the topology of polynomials with bounded integer coefficients. J. Eur. Math. Soc. 18 (2016), no. 1, 181--193.
  20. Self-similar subsets of Cantor sets. Adv. Math. 281 (2015), 857--885. (with Hui Rao and Yang Wang)
  21. Affine embeddings and intersections of Cantor sets J. Math. Pures Appl. 102 (2014), no. 6, 1062--1079. (with Wen Huang and Hui Rao)
  22. Non-conformal repellers and the continuity of pressure for matrix cocycles Geom. Funct. Anal. 24 (2014), 1101--1128. (with Pablo Shmerkin)
  23. Partition functions in numeration systems with bounded multiplicity. Uniform Distribution Theory 9 (2014), 43--77. (with Pierre Liardet and Alan Thomas)
  24. Local conical dimensions for measures. Math. Proc. Cambridge Philos. Soc., 154 (2013), 465--479 (with Antti Kaenmaki and Ville Suomala)
  25. Multifractal formalism for almost all self-affine measures. Comm. Math. Phys., 318 (2013), 473--504 (with Julien Barral)
  26. Variational principles for topological entropies of subsets. Journal of Functional Analysis 263 (2012) 2228--2254 (with Wen Huang)
  27. Weighted thermodynamic formalism on subshifts and applications. Asian J. Math. 16 (2012), 319--352. (with Julien Barral)
  28. Multifractal analysis of Bernoulli convolutions associated with Salem numbers. Adv. Math. 229 (2012), 3052--3077.
  29. Non-uniqueness of ergodic measures with full Hausdorff dimensions on a Gatzouras-Lalley carpet. Nonlinearity 24 (2011), 2563--2567. (with Julien Barral)
  30. Equilibrium states of the pressure function for products of matrices Discrete Contin. Dyn. Syst. 30 (2011), 699--708. (with Antti Kaenmaki)
  31. Growth rate for Beta expansions. Monatsh. Math. 162 (2011), 41--60. (with Nikita Sidorov)
  32. Equilibrium states for factor maps between subshifts. Adv. Math. 226 (2011) 2470--2502
  33. Lyapunov spectrum of asymptotically sub-additive potentials. Comm. Math. Phys. 297 (2010), 1--43 (with Wen Huang)
  34. On the Structures of Generating Iterated Function Systems of Cantor Sets. Adv. Math. 222 (2009) 1964--1981 (with Yang Wang)
  35. Dimension theory of iterated function systems. Comm. Pure Appl. Math. 62 (2009), 1435--1500 (with Huyi Hu)
  36. Multifractal formalism for Self-similar measures with weak separation condition. Journal de Mathematiques Pures et Appliquees 92 (2009), 407--428 (with Ka-Sing Lau)
  37. Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages. Ergodic theory and dynamical systems. 29 (2009), 885--918. (with Lin Shu)
  38. Lyapunov exponents for products of matrices and Multifractal analysis. Part II: General matrices. Israel J. of Math. 170 (2009), 355-394
  39. The thermodynamic formalism for sub-additive potentials. Discrete Contin. Dyn. Syst. 20 (2008), 639-657 (with Yong-Luo Cao and Wen Huang)
  40. When is the union of two unit intervals a self-similar set satisfying the open set condition? Monatsh. Math. 152 (2007), 125-134 (with Su Hua and Yuan Ji)
  41. Refinable functions with non-integer dilations. J. Func. Anal. 250 (2007), 1-20 (with Xin-Rong Dai and Yang Wang)
  42. Structure of refinable splines. Applied and Computational Harmonic Analysis 22 (2007): 374-381 (with Xin-Rong Dai and Yang Wang)
  43. Gibbs properties of self-conformal measures and the multifractal formalism. Ergodic theory and Dynamical Systems. 27 (2007), 787-812
  44. Classification of Refinable Splines. Constr. Approx. 24 (2006): 187-200 (with Xin-Rong Dai and Yang Wang)
  45. Generation of Finite Tight Frames by Householder Transformations. Adv. Comput. Math. 24 (2006): 297-309 (with Long Wang and Yang Wang)
  46. A Class of Self-Affine Sets and Self-Affine Measures. J. Four. Anal. Appl. 11 (2005), 107-124. (with Yang Wang)
  47. The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers. Adv. Math. 195 (2005), 24-101. Old Version in 1999: Part (I). Part (II).
  48. On statistical framework for estimation from random set observations. J. Theoret. Probab. 17 (2004) 85-110 (with Ding Feng)
  49. Bernoulli convolution associated with non-Pisot numbers. Adv. Math. 187 (2004), 173-194 (with Yang Wang)
  50. The variational principle for products of non-negative matrices. Nonlinearity 17 (2004) 447--457.
  51. Lyapunov exponent for products of matrices and Multifractal analysis. Part I: Positive matrices. Israel J. of Math., 138 (2003), pp. 353--376.
  52. Multifractal Analysis of the Weak Gibbs Measures and phase transition--application to some Bernoulli convolutions. Ergodic Theory & Dynamical System 23 (2003) 1751--1784 (with Eric Olivier)
  53. The smoothness of $L^q$-spectrum of self-similar measures with overlaps. J. Lond. Math. Soc. . 68 (2003), no. 1, 102--118.
  54. The exact packing measure of linear Cantor sets. Math. Nachr. 248-249(2003), 102--103.
  55. Convolutions of equicontractive self-similar measures on the line. Illinois Journal of Mathematics. 46 (2002), no. 4, 1339--1351.(with Nhu T. Nguyen and Tonghui Wang)
  56. On a property of Pisot numbers. J. Number Theory. 97 (2002), 305--316 (with Zhi-Ying Wen)
  57. Pressure Function for Products of Non-negative Matrices. Math. Research Lett. 9 (2002), no. 2-3, 363--378. (with Ka-Sing Lau)
  58. Ergodic limits on the conformal repeller. Adv. Math. 169 (2002) 58-91. (with Ka-Sing Lau and Jun Wu)
  59. Comparing Hausdorff measures and packing measures on the line, Math. Nachr. 241 (2002), 65--72.
  60. Recurrence, dimension and entropy, J. Lond Math Soc. 64 (2001), no. 1, 229--244. (with Ai-Hua Fan and Jun Wu)
  61. The Hausdorff dimension of recurrent sets in symbolic spaces, Nonlinearity, 14(2001), 81-85. (with Jun Wu)
  62. On the distribution of long-term time averages on symbolic space, J. Statist. Phys, 99(2000), 813-856. (with Ai-Hua Fan)
  63. The pointwise densities of Cantor measure, J. Math. Anal. Appl., 250(2000), 692-705. (with Su Hua and Zhi-Ying Wen)
  64. Some relations between packing premeasure and packing measure, Bull. London Math. Soc., 31 (1999), 665-670 (with Su Hua and Zhi-Ying Wen)
  65. On the limit Rademacher functions and Bernoulli convolutions, Dynamical Systems, Proceedings of the International Conference in Honor of Professor Liao Shantao, World Scientific, Singapore, 1999, pp. 46--49
  66. Analyse multifractale de la recurrence sur l'espace symbolique, C. R. Acad. Sci. Paris Ser. I Math. 327(1998), 629-632. (with Ai-Hua Fan)
  67. Category and dimension of compact subsets of ${\bf R}^n$, Chinese Sci. Bull. 42(1997), 1680-1683. (With Jun Wu).
  68. The net measure properties of symmetric Cantor sets and their applications, Progr. Natur. Sci., 7(1997), 172-178. (With Hui Rao and Jun Wu)
  69. Some dimensional results for homogeneous Moran sets, Sci. China Ser. A, 40(1997), 475-482. (With Zhi-Ying Wen and Jun Wu)

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